Bézier Curves-Based Optimal Trajectory Design for Multirotor UAVs with Any-Angle Pathfinding Algorithms

Abstract

Multirotor Unmanned Aerial Vehicles (UAVs) play an imperative role in many real-world applications in a variety of scenarios characterized by a high density of obstacles with different heights. Due to the complicated operation areas of UAVs and complex constraints associated with the assigned mission, there should be a suitable path to fly. Therefore, the most relevant challenge is how to plan a flyable path for a UAV without collisions with obstacles. This paper demonstrates how a flyable and continuous trajectory was constructed by using any-angle pathfinding algorithms, which are Basic Theta*, Lazy Theta*, and Phi* algorithms for a multirotor UAV in a cluttered environment. The three algorithms were modified by adopting a modified cost function during their implementation that considers the elevation of nodes. First, suitable paths are generated by using a modified version of the three algorithms. After that, four Bézier curves-based approaches are proposed to smooth the generated paths to be converted to flyable paths (trajectories). To determine the most suitable approach, particularly when searching for an optimal and collision-free trajectory design, an innovative evaluation process is proposed and applied in a variety of different size environments. The evaluation process results show high success rates of the four approaches; however, the approach with the highest success rate is adopted. Finally, based on the results of the evaluation process, a novel algorithm is proposed to increase the efficiency of the selected approach to the optimality in the construction process of the trajectory.

Keywords

• path planning
• trajectory planning
• Basic Theta*
• Lazy Theta*
• Phi*
• Bézier curves